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Journal for Geometry and Graphics 7 (2003), No. 2, 145--156
Copyright Heldermann Verlag 2003
Shapes of Space Curves
Radostina Encheva
Faculty of Mathematics and Informatics, Shumen University, Alen Mak Str. 115, Shumen 9712,
Bulgaria,
r.encheva@fmi.shu-bg.net
Georgi Georgiev
Faculty of Mathematics and Informatics, Shumen University, Alen Mak Str. 115, Shumen 9712,
Bulgaria,
g.georgiev@shu-bg.net
We study an ordered pair of functions which determines a regular space
curve up to a direct similarity. The first function is called a shape
curvature and the second one a shape torsion. We prove an extension of
the fundamental theorem of space curves relating to the group of direct
similarities. We also propose a direct way for recovering a space curve
from its shape curvature and shape torsion.
Keywords: space curves, direct similarities, differential-geometric invariants.
MSC: 53A55; 53A04.
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